Aggregate planning: overtime, temps or subcontracting?

A chair workshop in Binh Duong has 20 permanent workers, and its orders for the next six months are 1,400, 1,500, 1,900, 2,400, 2,800 and then 1,600 chairs. Normal capacity is 1,760 chairs a month. Orders in months 3, 4 and 5 exceed capacity, and by month 6 the workshop has spare time again. This is a hypothetical example and I set every number myself. How do you fill the gap at least cost?

What does aggregate planning decide, and where does it sit in the planning chain?

Aggregate planning strategies describes four approaches. Chase changes the workforce with demand by hiring and laying off. Flexibility keeps the people but varies hours. Level keeps output steady and uses stock as a buffer. Hybrid combines all three (Chopra, 2019, ch. 8; Slack et al., 2022, ch. 11). Aggregate planning sits at the start of the Planning sequence: aggregate plan, MPS, MRP, scheduling, looking up to about 18 months ahead, before the master production schedule, material requirements planning and detailed scheduling. Slack and colleagues record that early MRP II implementations were less effective because they ran from plans that could not be met (Slack et al., 2022, chs 10, 11, 14). As I read it, an error at the first step is inherited by every step after it.

What does each lever cost per chair?

My assumptions: wages of VND 40,000 an hour, 2 labour hours per chair, and a worker doing 22 days × 8 hours = 176 hours, or 88 chairs a month, for VND 7.04m a month. Overtime is paid at 1.5 times, capped at 20% of standard hours (352 chairs a month for the whole workshop). A temp is less productive, 75 chairs a month, paid VND 7.04m, plus VND 5m to recruit and train, on a short fixed-term contract. Subcontracting costs VND 135,000 a chair (we supply the materials) up to 800 chairs a month. Holding stock costs VND 6,000 a chair a month, and the warehouse takes at most 800 chairs.

Two rules follow. A temp is cheaper than subcontracting if kept two months or more (break-even about 1.6 months) and cheaper than overtime if kept three months or more (about 2.6). Building ahead is very cheap at VND 6,000 a chair a month, against the VND 40,000 gap between overtime and normal time, as long as there is room and the chair will not go out of fashion. Slack and colleagues note that perishable, fashion and made-to-order goods do not suit a level capacity plan (Slack et al., 2022, ch. 11).

What do four plans cost over the same six months?

Chase. The workers needed each month are 16, 18, 22, 28, 32 and 19. The workshop hires 16 times and lays off 17 times, at VND 5m per hire and VND 8m per layoff (assumptions). Wages of VND 950.4m, plus VND 80m for hiring and VND 136m for layoffs, make VND 1,166.4m. Chopra notes that this approach lowers morale and is hard to do at short notice (Chopra, 2019, ch. 8).

Level. With 22 workers, month 5 is still 320 chairs short. It takes 23 workers: wages of VND 971.5m plus VND 27.6m of holding cost, or VND 999.1m, before the VND 15m to recruit three more (VND 1,014.1m in all). But stock peaks at 1,272 chairs in month 3, over the 800-chair warehouse. If the space existed, this would come within 2% of the best plan for a 1,500-chair warehouse (VND 995.7m); with an 800-chair warehouse it is out.

Hybrid by hand. Keep 20 workers and run at full capacity for the first three months to build stock of 360, 620 and then 480 chairs, work 160 chairs of overtime in month 4 and 352 in month 5, and subcontract 688 chairs in month 5. Total: wages VND 844.8m, holding VND 8.8m, overtime VND 61.4m and subcontracting VND 92.9m, or VND 1,007.9m.

Solver. I ran an integer optimisation under the limits above. The result is about VND 997.8m: hire two temps from month 2 to month 5, work 248 chairs of overtime in month 4 and 352 in month 5, and subcontract nothing.

The components of this plan: permanent wages VND 844.8m, temps VND 66.3m, overtime VND 72.0m, holding VND 14.7m.

Chase costs about 17% more. The two hybrids are about 1% apart.

Which numbers change the plan?

I changed one assumption at a time and re-ran the solver:

Every result in the table lies between 1.5% below and 3.8% above the default. Two things stand out. First, when a temp costs VND 12m to recruit instead of VND 5m, the solver stops hiring temps, so the result equals the no-temps case. Second, in these two tests, cutting the warehouse to 300 chairs raised the total by 3.8%, more than the 3.0% from a holding cost 3.3 times higher; the comparison depends on the sizes of change I chose, so do not read it as a general rule.

What can you do with this in your own workshop?

The marginal-cost method does not change when the numbers do. Three steps: first, work out the extra cost per unit of each lever and the time you would use it; second, write down the hard limits (overtime cap, warehouse, subcontract agreement); third, try the four pure plans and then a blend, and see which one a hard limit rules out. The library's framework also warns against applying one pure strategy to every product line (Slack et al., 2022, ch. 11).

This is my reading of the example, not a conclusion from the textbooks: when the demand peak lasts only two to four months, it is hard to justify hiring and then laying off permanent workers, because the layoff cost and the morale risk outweigh the gain. Temps and overtime have clear time limits, so they carry the peak.

Going deeper: what did I read, and what did I not?

I have not read Chopra's chapter 8 or Slack and colleagues' chapters 10, 11 and 14 directly. The description of the four plan types, the cautions about perishable and made-to-order goods, the remark on staff morale and the steps of the planning chain come from the framework summaries already published on the site, so the citations to these two books are second-hand: I have not checked them against the books. All the figures in the post, from wage rates to capacity and costs, are my own assumptions; the results come from my own mixed-integer linear optimisation, checked by hand on the simpler plans. The model leaves out much that is real: new workers' gradual learning curve, leave, transport between the workshop and subcontractors, and the chance that stock goes out of fashion. It also assumes demand is known exactly six months ahead, which is rarely true.